Equivalence groupoid of generalized potential Burgers equations

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Pocheketa, Oleksandr A.^1

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivska Str., Kyiv

01601, Ukraine^1

关键词: Burgers equations;    Complicated structures;    Generalized Burgers Equation;    Groupoid;    Point transformations;    Second-order evolution equations;    Variable coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012011/pdf
DOI  :  10.1088/1742-6596/621/1/012011

来源: IOP

【 摘 要 】

We find the equivalence groupoid of a class of (1 + 1)-dimensional second-order evolution equations, which are called generalized potential Burgers equations. This class is related via potentialization with two classes of variable-coefficient generalized Burgers equations. Its equivalence groupoid is of complicated structure and is described via partitioning the entire class into three normalized subclasses such that there are no point transformations between equations from different subclasses. For each of these subclasses we construct its equivalence group of an appropriate kind.